Question: Simplify; express your answer in exponential form. Assume $z\neq 0, t\neq 0$. $\dfrac{{(z^{2})^{4}}}{{(z^{-2}t^{4})^{-2}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${z^{2}}$ to the exponent ${4}$ . Now ${2 \times 4 = 8}$ , so ${(z^{2})^{4} = z^{8}}$ In the denominator, we can use the distributive property of exponents. ${(z^{-2}t^{4})^{-2} = (z^{-2})^{-2}(t^{4})^{-2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(z^{2})^{4}}}{{(z^{-2}t^{4})^{-2}}} = \dfrac{{z^{8}}}{{z^{4}t^{-8}}}$ Break up the equation by variable and simplify. $\dfrac{{z^{8}}}{{z^{4}t^{-8}}} = \dfrac{{z^{8}}}{{z^{4}}} \cdot \dfrac{{1}}{{t^{-8}}} = z^{{8} - {4}} \cdot t^{- {(-8)}} = z^{4}t^{8}$.